10.1Vis_04

Data VisualizationData Visualization

Lecture 10Flow Visualization – Part 2

- Image-based Methods

- Critical Point Methods

10.2Vis_04

Flow Visualization - Texture Effects

Flow Visualization - Texture Effects

A new class of image-based methods attempts to visualize flow as a texturing effect

Most successful for 2D flow - and also for flow over surfaces in 3D

Methods include:– spot noise– line integral convolution - lic

10.3Vis_04

Spot Noise for Flow Visualization

Spot Noise for Flow Visualization

Spots of random size and intensity drawn in a plane give a texture effect

Texture defined as an intensity function f:f( x ) = ai h( x - xi )

where xi is random position, ai is random scale (zero mean), and h is the spot function - zero everywhere except for small area (here circular)

one spot many spots spot texture

10.4Vis_04

Spot Noise for Flow Visualization

Spot Noise for Flow Visualization

Different textures result from different spot shapes

Aligning the shape of the spot with the direction of flow gives a good visualization effect

In direction of flow, scale proportional to ( 1 + |v | ) , |v| = velocity magnitude

At 90 degrees to flow, scale proportional to 1 / ( 1 + | v | )

10.5Vis_04

Spot Noise ExampleSpot Noise Example

10.6Vis_04

Flow Over a SurfaceFlow Over a Surface

Wall friction displayedusing oil and paint - windevaporates oil and paintleaves white traces

Numerical simulationof flow, visualizedusing spot noise

10.7Vis_04

Spot Noise ExampleSpot Noise Example

10.8Vis_04

Spot Noise MovieSpot Noise Movie

10.9Vis_04

Learning More about Spot Noise

Learning More about Spot Noise

Spot noise has been developed by researchers in the Netherlands– van Wijk and de Leeuw– see

http://www.cwi.nl/~wimc/spotnoise.html

– Thanks to Wim de Leeuw for the images used in these slides

– Thanks to Jack van Wijk for the movie– http://www.win.tue.nl/~vanwijk

10.10Vis_04

Line Integral Convolution (LIC)

Line Integral Convolution (LIC)

Essence of method is:– consider a white noise texture,

T(x,y)– for each pixel, set its intensity as a

function (eg average) of values of T along a short streamline segment through the pixel

– this has effect of correlating the resulting pixel values along streamlines, so a sense of the flow direction is obtained

whitenoise

flowlines LIC

10.11Vis_04

LIC ExampleLIC Example

Flow over surface of car - from CIRA, ItalyItalian Aerospace Research Centre

10.12Vis_04

LIC ExampleLIC Example

Flow underneath car - from CIRA, Italy

10.13Vis_04

LIC MovieLIC Movie

10.14Vis_04

LIC Developments -Oriented LIC

LIC Developments -Oriented LIC

Original LIC shows direction of flow but not orientation (ie -> or <- )

Oriented LIC uses a sparse texture and a weighting of samples along streamline to give orientation effect

10.15Vis_04

Image-based Methods over Surfaces

Image-based Methods over Surfaces

10.16Vis_04

Learning More about LIC and Image-based Flow VisLearning More about LIC

and Image-based Flow Vis

Original LIC– B Cabral and C Leedom, Imaging Vector Fields

Using Line Integral Convolution, SIGGRAPH93, ACM Computer Graphics, pp263-270, 1993

Oriented LIC– R Wegenkittl and E Groller– www.cg.tuwien.ac.at/research/vis/dynsys/frolic/

Image-based flow visualization generally– Jack van Wijk – thanks to Jack for the surface

based movies

10.17Vis_04

Vector Field TopologyVector Field Topology

This approach aims to visualize only the significant features of a flow field

It identifies critical points– points where velocity magnitude is

zero– point of repulsion, attraction or a

saddle point– streamlines from critical points

divide space into regions of similar behaviour

10.18Vis_04

Characterising a Critical Point

Characterising a Critical Point

Let u = velocity in x; v = velocity in y

Look at Jacobian matrix:

du / dx du / dydv / dx dv / dy

The critical points are characterised by theeigenvalues of this matrix:

a1 + i b1 a2 - i b2

partialderivatives

10.19Vis_04

Characterising a Critical Point

Characterising a Critical Point

Sign of real part indicates:– repulsion a1, a2 positive

– attraction a1, a2 negative

– saddle a1, a2 opposite signs

– centre a1, a2 zero Imaginary part indicates rotation of

flow about critical point:– no rotation b1, b2 zero (node)

– rotation b1,b2 non-zero(focus)

10.20Vis_04

Attachment and Detachment Points

Attachment and Detachment Points

There are also critical points along surfaces, where streamlines start (detachment points) or end (attachment points)

The flow field topology is produced by:– identifying critical points– drawing streamlines from detachment or

attachment points and saddles (4 from saddles)... to repulsors and attractors

– drawing streamlines to/from critical points that exit boundary

10.21Vis_04

Vector Field TopologyVector Field Topology

In 3D, similar analysis can be carried out - we get stream surfaces separating flow field into uniform regions

Reading:– J Helman and L Hesselink, Representation

and Display of Vector Field Topology in Fluid Flow Data Sets, in Visualization in Scientific Computing, IEEE Press 1990

– http://science.nas.nasa.gov/Groups/VisTech/other/topology

10.22Vis_04

Flow Topology on SurfaceFlow Topology on Surface

10.23Vis_04